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Model to interpret pulsed-field-gradient NMR data including memory and superdispersion effects.

Marie-Christine Néel1, Daniela Bauer2, Marc Fleury2

  • 1Université d'Avignon et des Pays de Vaucluse, UMR 1114 EMMAH, F-84018 Avignon Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

We developed a new model for interpreting Nuclear Magnetic Resonance (NMR) velocimetry data. This versatile tool quantifies dispersion in porous media, improving flow analysis in various conditions.

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Area of Science:

  • Geophysics
  • Physical Chemistry
  • Fluid Dynamics

Background:

  • Quantitative interpretation of Nuclear Magnetic Resonance (NMR) velocimetry data is crucial for understanding fluid flow in porous media.
  • Existing models may not fully capture complex flow behaviors, including intermittent low velocities and rare high-velocity events.

Purpose of the Study:

  • To propose a versatile model for the quantitative interpretation of NMR velocimetry data.
  • To incorporate mechanisms of random arrests and long displacements into dispersion theory.
  • To provide analytical expressions for NMR signals based on subordinated Lévy processes.

Main Methods:

  • Utilized the Lagrangian form of dispersion theory with mobile/immobile tracer particles.
  • Incorporated independent random arrests and rare long displacements to simulate complex flow.
  • Derived analytical expressions for pulsed-field-gradient NMR signals.
  • Applied the model to NMR data from water flow in a homogeneous grain pack column.

Main Results:

  • The model provides a framework for quantitative interpretation of NMR velocimetry data.
  • Analytical expressions for NMR signals were derived based on subordinated Lévy processes.
  • Demonstrated the model's utility in quantifying dispersion for single- and two-phase flow.

Conclusions:

  • The proposed model offers a versatile approach for interpreting NMR velocimetry data.
  • It effectively quantifies dispersion in porous media by accounting for complex flow dynamics.
  • The model is applicable to both single- and two-phase flow conditions.